Is it possible to use only C++ to create iOS apps? Is there any downside to that? I read somewhere that you have to use a mix of objective C and C++ if you want to use C++ that bad.
I'll add a bit more color to the explanation given by Paul above.
There are two main areas where you must interface your c++ with ObjC to make a functional app:
You must interface with the runloop provided by UIKit to receive event notifications such as touches and app state changes.
To display content on screen, you need to either wrap UIKit / CoreAnimation or provide content via the EAGL / GLKit apis (OpenGL ES).
If you want access other capabilities of the device, they're typically only provided via an ObjC api, though sometimes they are also available at a lower level with a C API (such as audio and the address book).
In general, I tend to make most of the app ObjC, but then use C++ to help with the efficient implementation of some subsystems. In general, modern ObjC plays very well with C++ as they use both internally at Apple.
For the user interface on iOS you need objective C, for the remainder you can use C++. Wether or not using C++/Obj C and not pure objective C depends primarily on your C++ skills. If you are already fluent in C++, doing part of the development in that might pay off. If not, going for pure obj C is probably a better choice. See also